LATENT VOTE INVERSION AND VOTING RULE COMPARISON UNDER RULE CONSTRAINTS

Abstract

Using 34 seasons of panel data from Dancing with the Stars, this study develops a rule-constrained latent vote inversion model with entropy regularization to reconstruct unobservable weekly audience vote shares from observed elimination outcomes. Model validation yields a high consistency rate of 99.62%, and an entropy-based metric further reveals that audience preferences are generally diffuse and uncertain. Through counterfactual simulations, we systematically compare rank-based and percentage-based aggregation rules. The results indicate that switching from rank-based to percentage-based rules leads to a 10.34% outcome reversal rate, while the reverse switch only causes a 1.21% reversal, confirming that the percentage-based system significantly amplifies audience influence and favors high-popularity contestants. Mechanistic analysis demonstrates that the percentage-based rule preserves vote magnitude differences, whereas the rank-based rule compresses extreme popularity advantages into ordinal rankings. These findings quantify the systemic biases of different voting rules and offer empirical evidence for designing fairer and more balanced competition mechanisms.